Question

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directions: solve each question. your selected answer choice will indicate the color to use for the corresponding regions on the coloring page that match the question number.

1. a survey of 200 people attending a thanksgiving dinner asked about their favorite thanksgiving dish and whether they preferred white meat or dark meat turkey. the results are shown in the table.

what proportion of people who prefer white meat turkey also chose turkey as their favorite dish?

1. a local bakery sold a variety of thanksgiving pies. the distribution of the number of pies sold each day during november is approximately normal with a mean of 24 pies and a standard deviation of 5 pies.

what is the approximate number of pies sold on a day when the sales were at the 79th percentile?

1. a bakery offers three types of thanksgiving pies: pumpkin, apple, and pecan. 50% of their customers prefer pumpkin pie, 30% prefer apple pie, and 20% prefer pecan pie. if three customers are randomly selected, what is the probability that at least one of them prefers pecan pie?

Explanation:

Question 1

Step1: Identify relevant counts

From the table, the number of people who prefer white meat turkey and chose turkey as favorite dish is 50 (White Meat column, Turkey row). The total number of people who prefer white meat turkey is 110 (Total row, White Meat column).

Step2: Calculate the proportion

The proportion is the number of favorable cases (white meat + turkey) divided by the total number of white meat preferrers. So, the proportion is $\frac{50}{110} \approx 0.45$? Wait, no, wait: Wait, the table: Let me re - check. Wait, the first table: Favorite Dish: Turkey, White Meat: 50, Dark Meat: 30, Total: 80. Stuffing: White 30, Dark 20, Total 50. Mashed Potatoes: White 20, Dark 30, Total 50. Cranberry Sauce: White 10, Dark 10, Total 20. Total: White 110, Dark 90, Total 200. So, the number of people who prefer white meat and chose turkey is 50. The total number of people who prefer white meat is 110. So the proportion is $\frac{50}{110}\approx0.45$? Wait, but 50 divided by 110 is approximately 0.4545, which is close to 0.45 (option C). Wait, but let's recalculate: 50/110 = 5/11 ≈ 0.4545, so approximately 0.45.

Step1: Recall the z - score for the 79th percentile

We know that for a normal distribution, we can use the z - table. The 79th percentile means that 79% of the data is below this value. Looking up in the z - table, the z - score corresponding to a cumulative probability of 0.79 is approximately 0.81 (since $P(Z < 0.81)\approx0.7910$).

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know that $\mu = 24$, $\sigma = 5$, and $z = 0.81$. Rearranging the formula for $x$: $x=\mu+z\sigma$.
Substitute the values: $x = 24+0.81\times5=24 + 4.05=28.05\approx28$.

Step1: Find the probability of the complement event

The probability that a customer does not prefer pecan pie is $1 - 0.2=0.8$ (since 20% prefer pecan pie, so 80% do not).

Step2: Probability that all three do not prefer pecan pie

Since the selections are independent, the probability that all three customers do not prefer pecan pie is $0.8\times0.8\times0.8 = 0.8^{3}=0.512$.

Step3: Find the probability of at least one

The probability of at least one customer preferring pecan pie is the complement of the event that none prefer pecan pie. So, $P(\text{at least one})=1 - P(\text{none})=1 - 0.512 = 0.488$? Wait, no: Wait, the probability that a customer prefers pecan pie is 0.2, so the probability that a customer does not prefer pecan pie is 0.8. The probability that all three do not prefer pecan pie is $0.8\times0.8\times0.8 = 0.512$. Then the probability that at least one prefers pecan pie is $1 - 0.512 = 0.488$? Wait, no, wait: Wait, 1 - 0.512 = 0.488? Wait, no, 1 - 0.512 is 0.488? Wait, 0.8^3 is 0.512, so 1 - 0.512 = 0.488? But wait, the options: option C is 0.488. Wait, but let's re - check: The probability that a customer does not like pecan is 0.8. For three customers, the probability that all three do not like pecan is $0.8\times0.8\times0.8 = 0.512$. Then the probability that at least one likes pecan is $1 - 0.512 = 0.488$, which is option C. Wait, no, wait: Wait, the options are (A) 0.008, (B) 0.092, (C) 0.488, (D) 0.512, (E) 0.992. So the correct answer is C? Wait, no, wait: Wait, 1 - 0.512 is 0.488, so yes.

Answer:

C. 0.45

Question 2